Electrical Energy and Electrical Potential

In order to bring two like charges near each other work must be done.   In order to separate two opposite charges, work must be done.  Remember that whenever work gets done, energy changes form. 
As something does work on the positive charge, he increases the energy of that charge.  The closer he brings it, the more electrical potential energy it has.   When he releases the charge, work gets done on the charge which changes its energy from electrical potential energy to kinetic energy.  Every time he brings the charge back, he does work on the charge.  If he brought the charge closer to the other object, it would have more electrical potential energy.  If he brought 2 or 3 charges instead of one, then he would have had to do more work so he would have created more electrical potential energy.  Electrical potential energy could be measured in Joules just like any other form of energy.
Since the electrical potential energy can change depending on the amount of charge you are moving, it is helpful to describe the electrical potential energy per unit of charge.  This is known as electrical potential (NOTE: this sounds very similar to electrical potential energy, but it is not!)  

 

As a formula it is written like this: 

The energy per unit of charge is often called voltage so it is symbolized with the capital letter V.   Work or energy can be measured in Joules and charge is measured in Coulombs so the electrical potential can be measured in Joules per Coulomb which has been defined as a volt.

In this example the amount of work done by the person is 30J, this is also the amount of electrical potential energy that is possessed by all three charges together.  The electrical potential (not energy) is the amount of energy per unit of charge. 

At the original position of the charges they have no energy, so they also have no electrical potential or 0 volts.  Once they are pulled apart, they have have an electrical potential of 10 volts.  We could say that the electrical potential difference from one point to the other is 10 volts. 
Keep in mind that the electrical potential describes the amount of energy per unit of charge.  This means that when one of the charges is released, the electric field will do 10 Joules of work on the charge so it will have a kinetic energy of 10 Joules the instant before it strikes the negative charge.


For things like batteries, we specify the potential difference of the charges within the battery.  So a "D-cell" has a rating of 1.5 volts which means that for every Coulomb of charge that moves from the negative side of the cell to the positive side will do 1.5 Joules worth of work.  A "AA-cell" also has a rating of 1.5 volts so each Coulomb of charge that moves from one side to the other can and will do 1.5 Joules worth of work.  The difference between the D-cell and the AA-cell is that the D-cell has more Coulombs worth of charge, so it will last longer.  The AA-cell may only light a light bulb for 15 minutes while the D-cell may keep the same bulb lit for several hours.  As a result of having more charge, the D-cell has more energy and can do more work, but it will still do work at the same rate (or has the same power) as the AA-cell.   Notice in the animation that every charge that passes through the light bulb does 1.5 joules worth of work which makes it heat up and give off light.  Contrast this with a wall outlet that has a potential difference of a 12 volt car battery.  In the 12 volt car battery, every coulomb of charge that moves from one side to the other does 12 Joules worth of work.  In a 120 volt electrical outlet, every Coulomb of charge does 120 Joules worth of work as it moves from one side of the outlet to the other.
Remember that 1Coulomb of charge is a large amount.   Also keep in mind that a Joule is a fairly large unit for work.  These units don't work well if we are dealing with a small amount of charge.  That is why we sometimes talk about the elementary charge (charge on 1 electron or proton) as another unit of charge.  When we use the elementary charge (e) we need a smaller unit to measure energy or work in.    The unit of the electron volt (eV) was developed.  The electron volt is not a smaller unit for volts!!!   It is a smaller unit for energy.  An electron volt is the amount of energy it takes to move an electron through a potential difference of 1volt. 
Notice that if we look at the equation again for potential difference but use units of elementary charges (e) and electron volts (eV), we still get units of volts (V) when we are done.

 Remember that:

1e = 1.6 x 10^-19C

this leads us to:

1eV = 1.6 x 10^-19J

This portion of the unit contains many easy places to develop misunderstandings.   They have all been addressed earlier on this page but here is a quick list of them.   Please go out of your way to keep these from becoming a misunderstanding for you:

• Electric Potential Energy is not   the same as Electrical Potential.
  • Electrical Potential can also be described by the terms, potential difference, voltage, potential drop, potential rise, electromotive force, and EMF.  These terms may differ slightly in meaning depending on the situation.
• The variable we use for potential difference is V and the unit for potential difference is also V (volts).  Don't let that confuse you when you see V = 1.5V
• The electron volt is not a smaller unit of the volt, it's a smaller unit of the Joule.